The area of a triangle with vertices A, B, C is given by - Vidyadip

MCQ

The area of a triangle with vertices A, B, C is given by

A
$|\overrightarrow{A B} \times \overrightarrow{A C}|$
B
$\frac{1}{8}|\overrightarrow{A C} \times \overrightarrow{A B}|$
C
$\frac{1}{4}|\overrightarrow{A C} \times \overrightarrow{A B}|$
✓
$\frac{1}{2}|\overrightarrow{A B} \times \overrightarrow{A C}|$

✓

Answer

Correct option: D.

$\frac{1}{2}|\overrightarrow{A B} \times \overrightarrow{A C}|$

(d) $\frac{1}{2}|\overrightarrow{A B} \times \overrightarrow{A C}|$
Explanation: The area of the parallelogram with adjacent sides $A B$ and $A C=|\overrightarrow{A B} \times \overrightarrow{A C}|$. Hence, the area of the triangle with vertices $A , B , C =\frac{1}{2}|\overrightarrow{A B} \times \overrightarrow{A C}|$.

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